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BRISBANE Jan 2 (Reuters) - Maria Sharapova rallied to beat Kaia Kanepi on Thursday and will meet Serena Williams in the Brisbane International semi-final knowing she must drastically improve to end her run of 13 straight defeats against the world number one.

Williams comfortably beat Slovakian Dominika Cibulkova 6-3 6-3 in 61 minutes, winning the first set without losing a point on serve - a feat she had not achieved since she was a junior.

Prior to this match, Sharapova was involved in an error-strewn battle as she came from a set down to defeat Estonia's Kanepi 4-6 6-3 6-2 in two hours.

In contrast to Williams' start, which she credited to the extra attention paid to her serve during the off-season, Sharapova's match began with four straight breaks of serve and she went on to total 17 unforced errors in the first set.

Had 2012 champion Kanepi been in better form herself - the match produced 66 clangers in total - the Sharapova-Williams semi-final match-up the tournament organisers had been hoping for would have been scuppered.

The Russian did improve as the match went on and in the third set her service accuracy improved to 84 percent, nearly double her efforts in the first two sets, but she knows her game needs plenty more improvement.

"You're going up against a great champion that's playing great tennis at the moment," Sharapova said.

"You know that you have to raise your level in order to beat her.

"I think the intensity level of our matches are always high. I think she goes up and wants to play the best tennis against me.

"That's certainly no secret because she shows that on the court."

Although the contests between the two have been one-sided, Sharapova herself says she needs "to win a few times in order to call it rivalry", the pair's frosty off-court relations ensured the clash is the biggest in the women's game.

When asked about her relationship with Williams following her victory over Kanepi, the Russian replied: "I have said everything I had to say about it."

The American, who has been at pains to discuss her more relaxed approach to tennis and life during the tournament, was slightly more forthcoming.

"I had a great talk with her," Williams said. "I don't have anything against her or anything."

Despite these protestations their body language is certain to be heavily scrutinised when they step onto Pat Rafter Arena on Friday. (Editing by Amlan Chakraborty)